Floating point inaccuracies, perspective projection

Newbie & Debugging Questions
#1

When I set the near pane to 2 and the far pane to 10, everything is displayed at (X, Y, 2).
When I set the near pane to 1 and the far pane to 100, everything is displayed at (X, Y, 1).
When I set the near pane to 1 and the far pane to 10, nothing at (X, Y, 1) is displayed.

I believe this is to do with floating point inaccuracies with my matrix multiplication. Is there anything I can do to solve this issue?

#2

It’s a silly idea, but could you make the position of the near plane very slightly < 1? If it’s issues with floating point, it might make a difference.